LMFDB - Embedded newform 35.6.a.c.1.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [35,6,Mod(1,35)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("35.1"); S:= CuspForms(chi, 6); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(35, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0])) N = Newforms(chi, 6, names="a")

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	35.a (trivial)

Newform invariants

comment:select newform

sage:traces = [3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$5.61343369345$
Analytic rank:	$0$
Dimension:	$3$
Coefficient field:	3.3.577880.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - 98x - 232 $ x^3 - 98*x - 232
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$10.9200$ of defining polynomial
Character	$\chi$	$=$	35.1

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+8.91996 q^{2} +13.7828 q^{3} +47.5657 q^{4} -25.0000 q^{5} +122.942 q^{6} +49.0000 q^{7} +138.845 q^{8} -53.0335 q^{9} -222.999 q^{10} -187.840 q^{11} +655.590 q^{12} +255.647 q^{13} +437.078 q^{14} -344.571 q^{15} -283.609 q^{16} -1104.53 q^{17} -473.057 q^{18} +2278.71 q^{19} -1189.14 q^{20} +675.359 q^{21} -1675.52 q^{22} -475.149 q^{23} +1913.68 q^{24} +625.000 q^{25} +2280.36 q^{26} -4080.18 q^{27} +2330.72 q^{28} -3047.37 q^{29} -3073.56 q^{30} +4779.97 q^{31} -6972.82 q^{32} -2588.96 q^{33} -9852.39 q^{34} -1225.00 q^{35} -2522.57 q^{36} -13604.7 q^{37} +20326.0 q^{38} +3523.54 q^{39} -3471.13 q^{40} +12567.3 q^{41} +6024.17 q^{42} +23949.3 q^{43} -8934.71 q^{44} +1325.84 q^{45} -4238.31 q^{46} +20926.4 q^{47} -3908.93 q^{48} +2401.00 q^{49} +5574.97 q^{50} -15223.6 q^{51} +12160.0 q^{52} +22526.7 q^{53} -36395.0 q^{54} +4695.99 q^{55} +6803.41 q^{56} +31407.1 q^{57} -27182.5 q^{58} +14021.5 q^{59} -16389.7 q^{60} -3611.32 q^{61} +42637.1 q^{62} -2598.64 q^{63} -53121.8 q^{64} -6391.18 q^{65} -23093.4 q^{66} -33402.0 q^{67} -52537.9 q^{68} -6548.90 q^{69} -10926.9 q^{70} -41567.8 q^{71} -7363.44 q^{72} +2922.09 q^{73} -121353. q^{74} +8614.27 q^{75} +108388. q^{76} -9204.14 q^{77} +31429.8 q^{78} +22335.7 q^{79} +7090.22 q^{80} -43349.3 q^{81} +112100. q^{82} +42634.0 q^{83} +32123.9 q^{84} +27613.3 q^{85} +213627. q^{86} -42001.4 q^{87} -26080.6 q^{88} -127049. q^{89} +11826.4 q^{90} +12526.7 q^{91} -22600.8 q^{92} +65881.5 q^{93} +186663. q^{94} -56967.8 q^{95} -96105.2 q^{96} +13277.9 q^{97} +21416.8 q^{98} +9961.79 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 6 q^{2} + 26 q^{3} + 112 q^{4} - 75 q^{5} - 96 q^{6} + 147 q^{7} - 120 q^{8} + 489 q^{9} + 150 q^{10} - 194 q^{11} + 2956 q^{12} + 1892 q^{13} - 294 q^{14} - 650 q^{15} + 1496 q^{16} - 184 q^{17}+ \cdots - 60752 q^{99}+O(q^{100}) $ 3 * q - 6 * q^2 + 26 * q^3 + 112 * q^4 - 75 * q^5 - 96 * q^6 + 147 * q^7 - 120 * q^8 + 489 * q^9 + 150 * q^10 - 194 * q^11 + 2956 * q^12 + 1892 * q^13 - 294 * q^14 - 650 * q^15 + 1496 * q^16 - 184 * q^17 - 6078 * q^18 + 1212 * q^19 - 2800 * q^20 + 1274 * q^21 - 872 * q^22 + 3188 * q^23 - 13920 * q^24 + 1875 * q^25 - 9836 * q^26 + 7910 * q^27 + 5488 * q^28 - 11332 * q^29 + 2400 * q^30 + 9200 * q^31 - 20256 * q^32 - 8278 * q^33 - 18492 * q^34 - 3675 * q^35 + 38236 * q^36 + 6042 * q^37 + 25520 * q^38 + 12842 * q^39 + 3000 * q^40 + 10442 * q^41 - 4704 * q^42 + 28112 * q^43 - 20436 * q^44 - 12225 * q^45 - 41856 * q^46 + 2330 * q^47 + 68808 * q^48 + 7203 * q^49 - 3750 * q^50 + 3622 * q^51 + 63524 * q^52 + 7190 * q^53 - 138960 * q^54 + 4850 * q^55 - 5880 * q^56 + 45508 * q^57 + 37260 * q^58 + 23760 * q^59 - 73900 * q^60 + 8722 * q^61 + 24848 * q^62 + 23961 * q^63 + 4976 * q^64 - 47300 * q^65 + 24368 * q^66 - 97572 * q^67 + 3564 * q^68 + 92596 * q^69 + 7350 * q^70 - 52816 * q^71 - 251640 * q^72 + 34870 * q^73 - 241892 * q^74 + 16250 * q^75 + 115256 * q^76 - 9506 * q^77 - 142096 * q^78 - 71546 * q^79 - 37400 * q^80 - 3957 * q^81 + 241908 * q^82 - 20920 * q^83 + 144844 * q^84 + 4600 * q^85 + 266024 * q^86 - 112298 * q^87 + 59200 * q^88 - 192622 * q^89 + 151950 * q^90 + 92708 * q^91 + 248952 * q^92 - 20392 * q^93 + 360128 * q^94 - 30300 * q^95 - 296256 * q^96 + 116320 * q^97 - 14406 * q^98 - 60752 * q^99

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	8.91996	1.57684	0.788420	−	0.615137i	$-0.210899\pi$
$2$	8.91996	1.57684	0.788420	+	0.615137i	$0.210899\pi$
$3$	13.7828	0.884169	0.442085	−	0.896973i	$-0.354239\pi$
$3$	13.7828	0.884169	0.442085	+	0.896973i	$0.354239\pi$
$4$	47.5657	1.48643
$5$	−25.0000	−0.447214
$5$	−25.0000	−0.447214
$6$	122.942	1.39419
$7$	49.0000	0.377964
$7$	49.0000	0.377964
$8$	138.845	0.767018
$9$	−53.0335	−0.218245
$10$	−222.999	−0.705185
$11$	−187.840	−0.468064	−0.234032	−	0.972229i	$-0.575192\pi$
$11$	−187.840	−0.468064	−0.234032	+	0.972229i	$0.575192\pi$
$12$	655.590	1.31425
$13$	255.647	0.419549	0.209774	−	0.977750i	$-0.432727\pi$
$13$	255.647	0.419549	0.209774	+	0.977750i	$0.432727\pi$
$14$	437.078	0.595990
$15$	−344.571	−0.395412
$16$	−283.609	−0.276962
$17$	−1104.53	−0.926950	−0.463475	−	0.886110i	$-0.653398\pi$
$17$	−1104.53	−0.926950	−0.463475	+	0.886110i	$0.653398\pi$
$18$	−473.057	−0.344138
$19$	2278.71	1.44812	0.724062	−	0.689735i	$-0.242273\pi$
$19$	2278.71	1.44812	0.724062	+	0.689735i	$0.242273\pi$
$20$	−1189.14	−0.664750
$21$	675.359	0.334185
$22$	−1675.52	−0.738062
$23$	−475.149	−0.187288	−0.0936440	−	0.995606i	$-0.529852\pi$
$23$	−475.149	−0.187288	−0.0936440	+	0.995606i	$0.529852\pi$
$24$	1913.68	0.678174
$25$	625.000	0.200000
$26$	2280.36	0.661562
$27$	−4080.18	−1.07713
$28$	2330.72	0.561817
$29$	−3047.37	−0.672869	−0.336435	−	0.941707i	$-0.609221\pi$
$29$	−3047.37	−0.672869	−0.336435	+	0.941707i	$0.609221\pi$
$30$	−3073.56	−0.623503
$31$	4779.97	0.893349	0.446674	−	0.894697i	$-0.352608\pi$
$31$	4779.97	0.893349	0.446674	+	0.894697i	$0.352608\pi$
$32$	−6972.82	−1.20374
$33$	−2588.96	−0.413848
$34$	−9852.39	−1.46165
$35$	−1225.00	−0.169031
$36$	−2522.57	−0.324405
$37$	−13604.7	−1.63374	−0.816872	−	0.576819i	$-0.804294\pi$
$37$	−13604.7	−1.63374	−0.816872	+	0.576819i	$0.804294\pi$
$38$	20326.0	2.28346
$39$	3523.54	0.370952
$40$	−3471.13	−0.343021
$41$	12567.3	1.16757	0.583783	−	0.811910i	$-0.301572\pi$
$41$	12567.3	1.16757	0.583783	+	0.811910i	$0.301572\pi$
$42$	6024.17	0.526956
$43$	23949.3	1.97525	0.987623	−	0.156846i	$-0.0501328\pi$
$43$	23949.3	1.97525	0.987623	+	0.156846i	$0.0501328\pi$
$44$	−8934.71	−0.695743
$45$	1325.84	0.0976021
$46$	−4238.31	−0.295323
$47$	20926.4	1.38182	0.690909	−	0.722942i	$-0.257211\pi$
$47$	20926.4	1.38182	0.690909	+	0.722942i	$0.257211\pi$
$48$	−3908.93	−0.244881
$49$	2401.00	0.142857
$50$	5574.97	0.315368
$51$	−15223.6	−0.819581
$52$	12160.0	0.623629
$53$	22526.7	1.10156	0.550780	−	0.834651i	$-0.314330\pi$
$53$	22526.7	1.10156	0.550780	+	0.834651i	$0.314330\pi$
$54$	−36395.0	−1.69847
$55$	4695.99	0.209325
$56$	6803.41	0.289906
$57$	31407.1	1.28039
$58$	−27182.5	−1.06101
$59$	14021.5	0.524404	0.262202	−	0.965013i	$-0.415551\pi$
$59$	14021.5	0.524404	0.262202	+	0.965013i	$0.415551\pi$
$60$	−16389.7	−0.587752
$61$	−3611.32	−0.124263	−0.0621314	−	0.998068i	$-0.519790\pi$
$61$	−3611.32	−0.124263	−0.0621314	+	0.998068i	$0.519790\pi$
$62$	42637.1	1.40867
$63$	−2598.64	−0.0824888
$64$	−53121.8	−1.62115
$65$	−6391.18	−0.187628
$66$	−23093.4	−0.652572
$67$	−33402.0	−0.909045	−0.454522	−	0.890735i	$-0.650190\pi$
$67$	−33402.0	−0.909045	−0.454522	+	0.890735i	$0.650190\pi$
$68$	−52537.9	−1.37784
$69$	−6548.90	−0.165594
$70$	−10926.9	−0.266535
$71$	−41567.8	−0.978614	−0.489307	−	0.872112i	$-0.662750\pi$
$71$	−41567.8	−0.978614	−0.489307	+	0.872112i	$0.662750\pi$
$72$	−7363.44	−0.167398
$73$	2922.09	0.0641781	0.0320890	−	0.999485i	$-0.489784\pi$
$73$	2922.09	0.0641781	0.0320890	+	0.999485i	$0.489784\pi$
$74$	−121353.	−2.57615
$75$	8614.27	0.176834
$76$	108388.	2.15253
$77$	−9204.14	−0.176912
$78$	31429.8	0.584933
$79$	22335.7	0.402654	0.201327	−	0.979524i	$-0.435475\pi$
$79$	22335.7	0.402654	0.201327	+	0.979524i	$0.435475\pi$
$80$	7090.22	0.123861
$81$	−43349.3	−0.734124
$82$	112100.	1.84107
$83$	42634.0	0.679298	0.339649	−	0.940552i	$-0.389692\pi$
$83$	42634.0	0.679298	0.339649	+	0.940552i	$0.389692\pi$
$84$	32123.9	0.496741
$85$	27613.3	0.414545
$86$	213627.	3.11465
$87$	−42001.4	−0.594930
$88$	−26080.6	−0.359014
$89$	−127049.	−1.70019	−0.850094	−	0.526631i	$-0.823455\pi$
$89$	−127049.	−1.70019	−0.850094	+	0.526631i	$0.823455\pi$
$90$	11826.4	0.153903
$91$	12526.7	0.158575
$92$	−22600.8	−0.278390
$93$	65881.5	0.789871
$94$	186663.	2.17891
$95$	−56967.8	−0.647620
$96$	−96105.2	−1.06431
$97$	13277.9	0.143285	0.0716426	−	0.997430i	$-0.477176\pi$
$97$	13277.9	0.143285	0.0716426	+	0.997430i	$0.477176\pi$
$98$	21416.8	0.225263
$99$	9961.79	0.102153
$100$	29728.5	0.297285
$101$	−134560.	−1.31254	−0.656272	−	0.754525i	$-0.727867\pi$
$101$	−134560.	−1.31254	−0.656272	+	0.754525i	$0.727867\pi$
$102$	−135794.	−1.29235
$103$	−126101.	−1.17119	−0.585594	−	0.810604i	$-0.699139\pi$
$103$	−126101.	−1.17119	−0.585594	+	0.810604i	$0.699139\pi$
$104$	35495.4	0.321802
$105$	−16884.0	−0.149452
$106$	200937.	1.73698
$107$	−194824.	−1.64506	−0.822531	−	0.568720i	$-0.807439\pi$
$107$	−194824.	−1.64506	−0.822531	+	0.568720i	$0.807439\pi$
$108$	−194077.	−1.60108
$109$	213435.	1.72068	0.860339	−	0.509722i	$-0.170252\pi$
$109$	213435.	1.72068	0.860339	+	0.509722i	$0.170252\pi$
$110$	41888.0	0.330072
$111$	−187511.	−1.44451
$112$	−13896.8	−0.104682
$113$	153621.	1.13176	0.565880	−	0.824488i	$-0.308537\pi$
$113$	153621.	1.13176	0.565880	+	0.824488i	$0.308537\pi$
$114$	280150.	2.01897
$115$	11878.7	0.0837578
$116$	−144950.	−1.00017
$117$	−13557.9	−0.0915644
$118$	125072.	0.826902
$119$	−54122.1	−0.350354
$120$	−47842.0	−0.303288
$121$	−125767.	−0.780916
$122$	−32212.8	−0.195943
$123$	173213.	1.03233
$124$	227363.	1.32790
$125$	−15625.0	−0.0894427
$126$	−23179.8	−0.130072
$127$	223543.	1.22985	0.614924	−	0.788586i	$-0.289187\pi$
$127$	223543.	1.22985	0.614924	+	0.788586i	$0.289187\pi$
$128$	−250714.	−1.35255
$129$	330089.	1.74645
$130$	−57009.1	−0.295859
$131$	−226357.	−1.15243	−0.576216	−	0.817297i	$-0.695471\pi$
$131$	−226357.	−1.15243	−0.576216	+	0.817297i	$0.695471\pi$
$132$	−123146.	−0.615154
$133$	111657.	0.547339
$134$	−297944.	−1.43342
$135$	102005.	0.481709
$136$	−153359.	−0.710988
$137$	−58436.2	−0.265999	−0.133000	−	0.991116i	$-0.542461\pi$
$137$	−58436.2	−0.265999	−0.133000	+	0.991116i	$0.542461\pi$
$138$	−58415.9	−0.261116
$139$	−326896.	−1.43507	−0.717535	−	0.696523i	$-0.754730\pi$
$139$	−326896.	−1.43507	−0.717535	+	0.696523i	$0.754730\pi$
$140$	−58267.9	−0.251252
$141$	288426.	1.22176
$142$	−370783.	−1.54312
$143$	−48020.6	−0.196376
$144$	15040.8	0.0604455
$145$	76184.4	0.300916
$146$	26064.9	0.101199
$147$	33092.6	0.126310
$148$	−647116.	−2.42844
$149$	−41732.6	−0.153996	−0.0769981	−	0.997031i	$-0.524534\pi$
$149$	−41732.6	−0.153996	−0.0769981	+	0.997031i	$0.524534\pi$
$150$	76838.9	0.278839
$151$	237948.	0.849259	0.424629	−	0.905367i	$-0.360404\pi$
$151$	237948.	0.849259	0.424629	+	0.905367i	$0.360404\pi$
$152$	316388.	1.11074
$153$	58577.3	0.202302
$154$	−82100.5	−0.278961
$155$	−119499.	−0.399518
$156$	167600.	0.551393
$157$	376331.	1.21849	0.609243	−	0.792983i	$-0.291473\pi$
$157$	376331.	1.21849	0.609243	+	0.792983i	$0.291473\pi$
$158$	199234.	0.634921
$159$	310482.	0.973965
$160$	174321.	0.538330
$161$	−23282.3	−0.0707882
$162$	−386674.	−1.15760
$163$	−604784.	−1.78292	−0.891459	−	0.453101i	$-0.850318\pi$
$163$	−604784.	−1.78292	−0.891459	+	0.453101i	$0.850318\pi$
$164$	597771.	1.73550
$165$	64724.0	0.185078
$166$	380293.	1.07115
$167$	−66189.0	−0.183652	−0.0918258	−	0.995775i	$-0.529270\pi$
$167$	−66189.0	−0.183652	−0.0918258	+	0.995775i	$0.529270\pi$
$168$	93770.3	0.256326
$169$	−305938.	−0.823979
$170$	246310.	0.653671
$171$	−120848.	−0.316046
$172$	1.13916e6	2.93606
$173$	267726.	0.680103	0.340052	−	0.940407i	$-0.389555\pi$
$173$	267726.	0.680103	0.340052	+	0.940407i	$0.389555\pi$
$174$	−374651.	−0.938111
$175$	30625.0	0.0755929
$176$	53272.9	0.129636
$177$	193257.	0.463662
$178$	−1.13327e6	−2.68093
$179$	−425882.	−0.993475	−0.496738	−	0.867901i	$-0.665469\pi$
$179$	−425882.	−0.993475	−0.496738	+	0.867901i	$0.665469\pi$
$180$	63064.4	0.145078
$181$	−143066.	−0.324594	−0.162297	−	0.986742i	$-0.551890\pi$
$181$	−143066.	−0.324594	−0.162297	+	0.986742i	$0.551890\pi$
$182$	111738.	0.250047
$183$	−49774.2	−0.109869
$184$	−65972.1	−0.143653
$185$	340117.	0.730633
$186$	587661.	1.24550
$187$	207475.	0.433872
$188$	995380.	2.05397
$189$	−199929.	−0.407119
$190$	−508151.	−1.02119
$191$	−451436.	−0.895391	−0.447695	−	0.894186i	$-0.647755\pi$
$191$	−451436.	−0.895391	−0.447695	+	0.894186i	$0.647755\pi$
$192$	−732169.	−1.43337
$193$	783634.	1.51433	0.757164	−	0.653225i	$-0.226584\pi$
$193$	783634.	1.51433	0.757164	+	0.653225i	$0.226584\pi$
$194$	118439.	0.225938
$195$	−88088.5	−0.165895
$196$	114205.	0.212347
$197$	701313.	1.28750	0.643749	−	0.765237i	$-0.277378\pi$
$197$	701313.	1.28750	0.643749	+	0.765237i	$0.277378\pi$
$198$	88858.7	0.161078
$199$	469668.	0.840733	0.420366	−	0.907354i	$-0.361902\pi$
$199$	469668.	0.840733	0.420366	+	0.907354i	$0.361902\pi$
$200$	86778.2	0.153404
$201$	−460374.	−0.803749
$202$	−1.20027e6	−2.06967
$203$	−149321.	−0.254321
$204$	−724121.	−1.21825
$205$	−314182.	−0.522151
$206$	−1.12482e6	−1.84678
$207$	25198.8	0.0408747
$208$	−72503.8	−0.116199
$209$	−428032.	−0.677814
$210$	−150604.	−0.235662
$211$	−40052.3	−0.0619329	−0.0309665	−	0.999520i	$-0.509859\pi$
$211$	−40052.3	−0.0619329	−0.0309665	+	0.999520i	$0.509859\pi$
$212$	1.07150e6	1.63739
$213$	−572922.	−0.865260
$214$	−1.73782e6	−2.59400
$215$	−598732.	−0.883357
$216$	−566513.	−0.826182
$217$	234219.	0.337654
$218$	1.90383e6	2.71324
$219$	40274.7	0.0567443
$220$	223368.	0.311146
$221$	−282371.	−0.388901
$222$	−1.67259e6	−2.27776
$223$	−388002.	−0.522483	−0.261241	−	0.965273i	$-0.584132\pi$
$223$	−388002.	−0.522483	−0.261241	+	0.965273i	$0.584132\pi$
$224$	−341668.	−0.454972
$225$	−33145.9	−0.0436490
$226$	1.37029e6	1.78460
$227$	749133.	0.964927	0.482463	−	0.875916i	$-0.339742\pi$
$227$	749133.	0.964927	0.482463	+	0.875916i	$0.339742\pi$
$228$	1.49390e6	1.90320
$229$	1.34662e6	1.69690	0.848449	−	0.529276i	$-0.177537\pi$
$229$	1.34662e6	1.69690	0.848449	+	0.529276i	$0.177537\pi$
$230$	105958.	0.132073
$231$	−126859.	−0.156420
$232$	−423113.	−0.516103
$233$	−287439.	−0.346862	−0.173431	−	0.984846i	$-0.555485\pi$
$233$	−287439.	−0.346862	−0.173431	+	0.984846i	$0.555485\pi$
$234$	−120936.	−0.144383
$235$	−523161.	−0.617968
$236$	666944.	0.779488
$237$	307849.	0.356014
$238$	−482767.	−0.552453
$239$	884752.	1.00191	0.500953	−	0.865475i	$-0.332983\pi$
$239$	884752.	1.00191	0.500953	+	0.865475i	$0.332983\pi$
$240$	97723.3	0.109514
$241$	226417.	0.251112	0.125556	−	0.992087i	$-0.459929\pi$
$241$	226417.	0.251112	0.125556	+	0.992087i	$0.459929\pi$
$242$	−1.12184e6	−1.23138
$243$	394008.	0.428045
$244$	−171775.	−0.184708
$245$	−60025.0	−0.0638877
$246$	1.54505e6	1.62781
$247$	582546.	0.607559
$248$	663676.	0.685215
$249$	587617.	0.600615
$250$	−139374.	−0.141037
$251$	153345.	0.153633	0.0768167	−	0.997045i	$-0.475524\pi$
$251$	153345.	0.153633	0.0768167	+	0.997045i	$0.475524\pi$
$252$	−123606.	−0.122614
$253$	89251.7	0.0876628
$254$	1.99399e6	1.93927
$255$	380590.	0.366528
$256$	−536461.	−0.511609
$257$	−979616.	−0.925174	−0.462587	−	0.886574i	$-0.653079\pi$
$257$	−979616.	−0.925174	−0.462587	+	0.886574i	$0.653079\pi$
$258$	2.94438e6	2.75388
$259$	−666629.	−0.617497
$260$	−304001.	−0.278895
$261$	161613.	0.146850
$262$	−2.01909e6	−1.81720
$263$	−796798.	−0.710328	−0.355164	−	0.934804i	$-0.615575\pi$
$263$	−796798.	−0.710328	−0.355164	+	0.934804i	$0.615575\pi$
$264$	−359464.	−0.317429
$265$	−563167.	−0.492632
$266$	995975.	0.863067
$267$	−1.75110e6	−1.50325
$268$	−1.58879e6	−1.35123
$269$	−4881.02	−0.00411273	−0.00205637	−	0.999998i	$-0.500655\pi$
$269$	−4881.02	−0.00411273	−0.00205637	+	0.999998i	$0.500655\pi$
$270$	909876.	0.759579
$271$	1.76108e6	1.45665	0.728325	−	0.685232i	$-0.240299\pi$
$271$	1.76108e6	1.45665	0.728325	+	0.685232i	$0.240299\pi$
$272$	313255.	0.256730
$273$	172654.	0.140207
$274$	−521249.	−0.419439
$275$	−117400.	−0.0936128
$276$	−311503.	−0.246144
$277$	65248.7	0.0510943	0.0255472	−	0.999674i	$-0.491867\pi$
$277$	65248.7	0.0510943	0.0255472	+	0.999674i	$0.491867\pi$
$278$	−2.91590e6	−2.26288
$279$	−253499.	−0.194969
$280$	−170085.	−0.129650
$281$	−1.29220e6	−0.976258	−0.488129	−	0.872772i	$-0.662320\pi$
$281$	−1.29220e6	−0.976258	−0.488129	+	0.872772i	$0.662320\pi$
$282$	2.57274e6	1.92652
$283$	−682719.	−0.506729	−0.253365	−	0.967371i	$-0.581537\pi$
$283$	−682719.	−0.506729	−0.253365	+	0.967371i	$0.581537\pi$
$284$	−1.97720e6	−1.45464
$285$	−785178.	−0.572606
$286$	−428342.	−0.309653
$287$	615796.	0.441298
$288$	369793.	0.262711
$289$	−199863.	−0.140763
$290$	679561.	0.474497
$291$	183008.	0.126688
$292$	138991.	0.0953961
$293$	1.19779e6	0.815102	0.407551	−	0.913183i	$-0.366383\pi$
$293$	1.19779e6	0.815102	0.407551	+	0.913183i	$0.366383\pi$
$294$	295184.	0.199171
$295$	−350539.	−0.234521
$296$	−1.88894e6	−1.25311
$297$	766419.	0.504168
$298$	−372253.	−0.242828
$299$	−121470.	−0.0785765
$300$	409744.	0.262851
$301$	1.17351e6	0.746573
$302$	2.12249e6	1.33915
$303$	−1.85462e6	−1.16051
$304$	−646263.	−0.401075
$305$	90283.0	0.0555720
$306$	522507.	0.318998
$307$	1.74933e6	1.05932	0.529658	−	0.848211i	$-0.322320\pi$
$307$	1.74933e6	1.05932	0.529658	+	0.848211i	$0.322320\pi$
$308$	−437801.	−0.262966
$309$	−1.73803e6	−1.03553
$310$	−1.06593e6	−0.629976
$311$	−281786.	−0.165203	−0.0826016	−	0.996583i	$-0.526323\pi$
$311$	−281786.	−0.165203	−0.0826016	+	0.996583i	$0.526323\pi$
$312$	489227.	0.284527
$313$	−1.14765e6	−0.662136	−0.331068	−	0.943607i	$-0.607409\pi$
$313$	−1.14765e6	−0.662136	−0.331068	+	0.943607i	$0.607409\pi$
$314$	3.35686e6	1.92136
$315$	64966.1	0.0368901
$316$	1.06241e6	0.598516
$317$	−2.82020e6	−1.57627	−0.788136	−	0.615501i	$-0.788954\pi$
$317$	−2.82020e6	−1.57627	−0.788136	+	0.615501i	$0.788954\pi$
$318$	2.76948e6	1.53579
$319$	572417.	0.314946
$320$	1.32805e6	0.725000
$321$	−2.68522e6	−1.45451
$322$	−207677.	−0.111622
$323$	−2.51691e6	−1.34234
$324$	−2.06194e6	−1.09122
$325$	159779.	0.0839098
$326$	−5.39465e6	−2.81138
$327$	2.94174e6	1.52137
$328$	1.74490e6	0.895544
$329$	1.02540e6	0.522278
$330$	577336.	0.291839
$331$	603651.	0.302842	0.151421	−	0.988469i	$-0.451615\pi$
$331$	603651.	0.302842	0.151421	+	0.988469i	$0.451615\pi$
$332$	2.02791e6	1.00973
$333$	721504.	0.356556
$334$	−590403.	−0.289589
$335$	835050.	0.406537
$336$	−191538.	−0.0925563
$337$	1.09597e6	0.525684	0.262842	−	0.964839i	$-0.415340\pi$
$337$	1.09597e6	0.525684	0.262842	+	0.964839i	$0.415340\pi$
$338$	−2.72895e6	−1.29928
$339$	2.11733e6	1.00067
$340$	1.31345e6	0.616191
$341$	−897867.	−0.418144
$342$	−1.07796e6	−0.498354
$343$	117649.	0.0539949
$344$	3.32524e6	1.51505
$345$	163722.	0.0740560
$346$	2.38810e6	1.07241
$347$	−2.53615e6	−1.13071	−0.565355	−	0.824848i	$-0.691261\pi$
$347$	−2.53615e6	−1.13071	−0.565355	+	0.824848i	$0.691261\pi$
$348$	−1.99783e6	−0.884321
$349$	−1.31958e6	−0.579927	−0.289963	−	0.957038i	$-0.593643\pi$
$349$	−1.31958e6	−0.579927	−0.289963	+	0.957038i	$0.593643\pi$
$350$	273174.	0.119198
$351$	−1.04309e6	−0.451911
$352$	1.30977e6	0.563429
$353$	1.68374e6	0.719181	0.359591	−	0.933110i	$-0.382916\pi$
$353$	1.68374e6	0.719181	0.359591	+	0.933110i	$0.382916\pi$
$354$	1.72384e6	0.731121
$355$	1.03920e6	0.437650
$356$	−6.04318e6	−2.52721
$357$	−745956.	−0.309772
$358$	−3.79885e6	−1.56655
$359$	−1.66512e6	−0.681882	−0.340941	−	0.940085i	$-0.610746\pi$
$359$	−1.66512e6	−0.681882	−0.340941	+	0.940085i	$0.610746\pi$
$360$	184086.	0.0748626
$361$	2.71643e6	1.09706
$362$	−1.27614e6	−0.511832
$363$	−1.73343e6	−0.690462
$364$	595841.	0.235710
$365$	−73052.3	−0.0287013
$366$	−443984.	−0.173247
$367$	−1.22452e6	−0.474570	−0.237285	−	0.971440i	$-0.576258\pi$
$367$	−1.22452e6	−0.474570	−0.237285	+	0.971440i	$0.576258\pi$
$368$	134756.	0.0518716
$369$	−666487.	−0.254815
$370$	3.03383e6	1.15209
$371$	1.10381e6	0.416350
$372$	3.13370e6	1.17409
$373$	3.14643e6	1.17097	0.585486	−	0.810683i	$-0.300904\pi$
$373$	3.14643e6	1.17097	0.585486	+	0.810683i	$0.300904\pi$
$374$	1.85067e6	0.684147
$375$	−215357.	−0.0790825
$376$	2.90553e6	1.05988
$377$	−779053.	−0.282302
$378$	−1.78336e6	−0.641961
$379$	3.25784e6	1.16502	0.582508	−	0.812825i	$-0.302071\pi$
$379$	3.25784e6	1.16502	0.582508	+	0.812825i	$0.302071\pi$
$380$	−2.70971e6	−0.962641
$381$	3.08105e6	1.08739
$382$	−4.02679e6	−1.41189
$383$	4.63245e6	1.61367	0.806833	−	0.590780i	$-0.201180\pi$
$383$	4.63245e6	1.61367	0.806833	+	0.590780i	$0.201180\pi$
$384$	−3.45555e6	−1.19588
$385$	230103.	0.0791173
$386$	6.98998e6	2.38785
$387$	−1.27011e6	−0.431087
$388$	631574.	0.212983
$389$	1.93239e6	0.647471	0.323735	−	0.946148i	$-0.395061\pi$
$389$	1.93239e6	0.647471	0.323735	+	0.946148i	$0.395061\pi$
$390$	−785746.	−0.261590
$391$	524818.	0.173607
$392$	333367.	0.109574
$393$	−3.11984e6	−1.01894
$394$	6.25568e6	2.03018
$395$	−558393.	−0.180072
$396$	473839.	0.151842
$397$	2.59643e6	0.826800	0.413400	−	0.910550i	$-0.364341\pi$
$397$	2.59643e6	0.826800	0.413400	+	0.910550i	$0.364341\pi$
$398$	4.18942e6	1.32570
$399$	1.53895e6	0.483940
$400$	−177255.	−0.0553923
$401$	−703617.	−0.218512	−0.109256	−	0.994014i	$-0.534847\pi$
$401$	−703617.	−0.218512	−0.109256	+	0.994014i	$0.534847\pi$
$402$	−4.10652e6	−1.26738
$403$	1.22199e6	0.374803
$404$	−6.40045e6	−1.95100
$405$	1.08373e6	0.328310
$406$	−1.33194e6	−0.401023
$407$	2.55550e6	0.764697
$408$	−2.11372e6	−0.628633
$409$	−6.16366e6	−1.82192	−0.910962	−	0.412491i	$-0.864659\pi$
$409$	−6.16366e6	−1.82192	−0.910962	+	0.412491i	$0.864659\pi$
$410$	−2.80249e6	−0.823350
$411$	−805416.	−0.235188
$412$	−5.99810e6	−1.74089
$413$	687056.	0.198206
$414$	224772.	0.0644528
$415$	−1.06585e6	−0.303791
$416$	−1.78258e6	−0.505029
$417$	−4.50556e6	−1.26884
$418$	−3.81803e6	−1.06881
$419$	3.63250e6	1.01081	0.505406	−	0.862882i	$-0.331343\pi$
$419$	3.63250e6	1.01081	0.505406	+	0.862882i	$0.331343\pi$
$420$	−803097.	−0.222149
$421$	−5.63096e6	−1.54838	−0.774190	−	0.632953i	$-0.781842\pi$
$421$	−5.63096e6	−1.54838	−0.774190	+	0.632953i	$0.781842\pi$
$422$	−357265.	−0.0976584
$423$	−1.10980e6	−0.301575
$424$	3.12772e6	0.844916
$425$	−690333.	−0.185390
$426$	−5.11044e6	−1.36438
$427$	−176955.	−0.0469669
$428$	−9.26692e6	−2.44527
$429$	−661860.	−0.173629
$430$	−5.34066e6	−1.39291
$431$	−1.22251e6	−0.317000	−0.158500	−	0.987359i	$-0.550666\pi$
$431$	−1.22251e6	−0.317000	−0.158500	+	0.987359i	$0.550666\pi$
$432$	1.15717e6	0.298325
$433$	5.89069e6	1.50989	0.754946	−	0.655787i	$-0.227663\pi$
$433$	5.89069e6	1.50989	0.754946	+	0.655787i	$0.227663\pi$
$434$	2.08922e6	0.532427
$435$	1.05004e6	0.266061
$436$	1.01522e7	2.55766
$437$	−1.08273e6	−0.271216
$438$	359249.	0.0894767
$439$	25.5425	6.32561e−6 0	3.16281e−6	−	1.00000i	$-0.499999\pi$
$439$	25.5425	6.32561e−6 0	3.16281e−6		1.00000i	$0.499999\pi$
$440$	652015.	0.160556
$441$	−127333.	−0.0311778
$442$	−2.51874e6	−0.613235
$443$	4.51430e6	1.09290	0.546451	−	0.837491i	$-0.315979\pi$
$443$	4.51430e6	1.09290	0.546451	+	0.837491i	$0.315979\pi$
$444$	−8.91909e6	−2.14715
$445$	3.17623e6	0.760347
$446$	−3.46096e6	−0.823872
$447$	−575194.	−0.136159
$448$	−2.60297e6	−0.612737
$449$	3.13133e6	0.733015	0.366507	−	0.930415i	$-0.380553\pi$
$449$	3.13133e6	0.733015	0.366507	+	0.930415i	$0.380553\pi$
$450$	−295660.	−0.0688275
$451$	−2.36063e6	−0.546496
$452$	7.30708e6	1.68228
$453$	3.27960e6	0.750888
$454$	6.68223e6	1.52154
$455$	−313168.	−0.0709167
$456$	4.36072e6	0.982079
$457$	926153.	0.207440	0.103720	−	0.994607i	$-0.466925\pi$
$457$	926153.	0.207440	0.103720	+	0.994607i	$0.466925\pi$
$458$	1.20118e7	2.67574
$459$	4.50669e6	0.998450
$460$	565019.	0.124500
$461$	1.78674e6	0.391570	0.195785	−	0.980647i	$-0.437275\pi$
$461$	1.78674e6	0.391570	0.195785	+	0.980647i	$0.437275\pi$
$462$	−1.13158e6	−0.246649
$463$	−4.33387e6	−0.939558	−0.469779	−	0.882784i	$-0.655666\pi$
$463$	−4.33387e6	−0.939558	−0.469779	+	0.882784i	$0.655666\pi$
$464$	864262.	0.186359
$465$	−1.64704e6	−0.353241
$466$	−2.56395e6	−0.546946
$467$	8.04215e6	1.70640	0.853198	−	0.521587i	$-0.174660\pi$
$467$	8.04215e6	1.70640	0.853198	+	0.521587i	$0.174660\pi$
$468$	−644889.	−0.136104
$469$	−1.63670e6	−0.343587
$470$	−4.66657e6	−0.974436
$471$	5.18691e6	1.07735
$472$	1.94682e6	0.402227
$473$	−4.49862e6	−0.924541
$474$	2.74600e6	0.561378
$475$	1.42420e6	0.289625
$476$	−2.57436e6	−0.520776
$477$	−1.19467e6	−0.240410
$478$	7.89195e6	1.57985
$479$	−5.75325e6	−1.14571	−0.572855	−	0.819657i	$-0.694164\pi$
$479$	−5.75325e6	−1.14571	−0.572855	+	0.819657i	$0.694164\pi$
$480$	2.40263e6	0.475975
$481$	−3.47800e6	−0.685436
$482$	2.01963e6	0.395963
$483$	−320896.	−0.0625888
$484$	−5.98221e6	−1.16077
$485$	−331948.	−0.0640791
$486$	3.51453e6	0.674958
$487$	−1.05952e6	−0.202435	−0.101217	−	0.994864i	$-0.532274\pi$
$487$	−1.05952e6	−0.202435	−0.101217	+	0.994864i	$0.532274\pi$
$488$	−501414.	−0.0953118
$489$	−8.33564e6	−1.57640
$490$	−535421.	−0.100741
$491$	2.61349e6	0.489235	0.244618	−	0.969620i	$-0.421338\pi$
$491$	2.61349e6	0.489235	0.244618	+	0.969620i	$0.421338\pi$
$492$	8.23897e6	1.53448
$493$	3.36593e6	0.623717
$494$	5.19629e6	0.958023
$495$	−249045.	−0.0456840
$496$	−1.35564e6	−0.247423
$497$	−2.03682e6	−0.369881
$498$	5.24152e6	0.947074
$499$	−7.96728e6	−1.43238	−0.716191	−	0.697904i	$-0.754116\pi$
$499$	−7.96728e6	−1.43238	−0.716191	+	0.697904i	$0.754116\pi$
$500$	−743214.	−0.132950
$501$	−912272.	−0.162379
$502$	1.36783e6	0.242255
$503$	2.56418e6	0.451885	0.225942	−	0.974141i	$-0.427454\pi$
$503$	2.56418e6	0.451885	0.225942	+	0.974141i	$0.427454\pi$
$504$	−360809.	−0.0632704
$505$	3.36401e6	0.586987
$506$	796122.	0.138230
$507$	−4.21669e6	−0.728537
$508$	1.06330e7	1.82808
$509$	−9.92048e6	−1.69722	−0.848610	−	0.529019i	$-0.822560\pi$
$509$	−9.92048e6	−1.69722	−0.848610	+	0.529019i	$0.822560\pi$
$510$	3.39485e6	0.577956
$511$	143183.	0.0242570
$512$	3.23764e6	0.545825
$513$	−9.29756e6	−1.55982
$514$	−8.73814e6	−1.45885
$515$	3.15253e6	0.523771
$516$	1.57009e7	2.59597
$517$	−3.93081e6	−0.646779
$518$	−5.94631e6	−0.973695
$519$	3.69002e6	0.601327
$520$	−887384.	−0.143914
$521$	−537196.	−0.0867039	−0.0433519	−	0.999060i	$-0.513804\pi$
$521$	−537196.	−0.0867039	−0.0433519	+	0.999060i	$0.513804\pi$
$522$	1.44158e6	0.231560
$523$	−1.69124e6	−0.270366	−0.135183	−	0.990821i	$-0.543162\pi$
$523$	−1.69124e6	−0.270366	−0.135183	+	0.990821i	$0.543162\pi$
$524$	−1.07668e7	−1.71301
$525$	422099.	0.0668369
$526$	−7.10740e6	−1.12007
$527$	−5.27964e6	−0.828090
$528$	734252.	0.114620
$529$	−6.21058e6	−0.964923
$530$	−5.02343e6	−0.776803
$531$	−743612.	−0.114449
$532$	5.31104e6	0.813580
$533$	3.21279e6	0.489851
$534$	−1.56197e7	−2.37039
$535$	4.87059e6	0.735694
$536$	−4.63770e6	−0.697254
$537$	−5.86986e6	−0.878400
$538$	−43538.5	−0.00648512
$539$	−451003.	−0.0668663
$540$	4.85191e6	0.716026
$541$	8.27002e6	1.21482	0.607412	−	0.794387i	$-0.292208\pi$
$541$	8.27002e6	1.21482	0.607412	+	0.794387i	$0.292208\pi$
$542$	1.57087e7	2.29690
$543$	−1.97185e6	−0.286996
$544$	7.70171e6	1.11581
$545$	−5.33588e6	−0.769511
$546$	1.54006e6	0.221084
$547$	−8.70811e6	−1.24439	−0.622193	−	0.782864i	$-0.713758\pi$
$547$	−8.70811e6	−1.24439	−0.622193	+	0.782864i	$0.713758\pi$
$548$	−2.77956e6	−0.395389
$549$	191521.	0.0271197
$550$	−1.04720e6	−0.147612
$551$	−6.94409e6	−0.974398
$552$	−909282.	−0.127014
$553$	1.09445e6	0.152189
$554$	582016.	0.0805676
$555$	4.68778e6	0.646003
$556$	−1.55490e7	−2.13313
$557$	9.16586e6	1.25180	0.625901	−	0.779903i	$-0.284732\pi$
$557$	9.16586e6	1.25180	0.625901	+	0.779903i	$0.284732\pi$
$558$	−2.26120e6	−0.307435
$559$	6.12256e6	0.828712
$560$	347421.	0.0468151
$561$	2.85959e6	0.383616
$562$	−1.15264e7	−1.53940
$563$	6.96113e6	0.925568	0.462784	−	0.886471i	$-0.346850\pi$
$563$	6.96113e6	0.925568	0.462784	+	0.886471i	$0.346850\pi$
$564$	1.37192e7	1.81606
$565$	−3.84052e6	−0.506138
$566$	−6.08983e6	−0.799031
$567$	−2.12412e6	−0.277473
$568$	−5.77149e6	−0.750615
$569$	−5.44814e6	−0.705452	−0.352726	−	0.935727i	$-0.614745\pi$
$569$	−5.44814e6	−0.705452	−0.352726	+	0.935727i	$0.614745\pi$
$570$	−7.00375e6	−0.902909
$571$	3.38027e6	0.433872	0.216936	−	0.976186i	$-0.430394\pi$
$571$	3.38027e6	0.433872	0.216936	+	0.976186i	$0.430394\pi$
$572$	−2.28413e6	−0.291898
$573$	−6.22206e6	−0.791677
$574$	5.49288e6	0.695857
$575$	−296968.	−0.0374576
$576$	2.81724e6	0.353807
$577$	4.09888e6	0.512537	0.256269	−	0.966606i	$-0.417507\pi$
$577$	4.09888e6	0.512537	0.256269	+	0.966606i	$0.417507\pi$
$578$	−1.78277e6	−0.221961
$579$	1.08007e7	1.33892
$580$	3.62376e6	0.447290
$581$	2.08906e6	0.256751
$582$	1.63242e6	0.199767
$583$	−4.23140e6	−0.515600
$584$	405718.	0.0492258
$585$	338947.	0.0409489
$586$	1.06842e7	1.28529
$587$	−4.79895e6	−0.574845	−0.287423	−	0.957804i	$-0.592798\pi$
$587$	−4.79895e6	−0.574845	−0.287423	+	0.957804i	$0.592798\pi$
$588$	1.57407e6	0.187750
$589$	1.08922e7	1.29368
$590$	−3.12679e6	−0.369802
$591$	9.66608e6	1.13837
$592$	3.85841e6	0.452485
$593$	−1.70681e6	−0.199319	−0.0996595	−	0.995022i	$-0.531775\pi$
$593$	−1.70681e6	−0.199319	−0.0996595	+	0.995022i	$0.531775\pi$
$594$	6.83643e6	0.794993
$595$	1.35305e6	0.156683
$596$	−1.98504e6	−0.228904
$597$	6.47335e6	0.743350
$598$	−1.08351e6	−0.123903
$599$	−6.81366e6	−0.775914	−0.387957	−	0.921677i	$-0.626819\pi$
$599$	−6.81366e6	−0.775914	−0.387957	+	0.921677i	$0.626819\pi$
$600$	1.19605e6	0.135635
$601$	−4.99344e6	−0.563915	−0.281957	−	0.959427i	$-0.590984\pi$
$601$	−4.99344e6	−0.563915	−0.281957	+	0.959427i	$0.590984\pi$
$602$	1.04677e7	1.17723
$603$	1.77142e6	0.198394
$604$	1.13182e7	1.26236
$605$	3.14418e6	0.349236
$606$	−1.65432e7	−1.82994
$607$	5.00268e6	0.551101	0.275550	−	0.961287i	$-0.411140\pi$
$607$	5.00268e6	0.551101	0.275550	+	0.961287i	$0.411140\pi$
$608$	−1.58891e7	−1.74317
$609$	−2.05807e6	−0.224863
$610$	805320.	0.0876282
$611$	5.34978e6	0.579740
$612$	2.78627e6	0.300707
$613$	5.71699e6	0.614492	0.307246	−	0.951630i	$-0.400593\pi$
$613$	5.71699e6	0.614492	0.307246	+	0.951630i	$0.400593\pi$
$614$	1.56039e7	1.67037
$615$	−4.33032e6	−0.461670
$616$	−1.27795e6	−0.135694
$617$	−6.02422e6	−0.637071	−0.318535	−	0.947911i	$-0.603191\pi$
$617$	−6.02422e6	−0.637071	−0.318535	+	0.947911i	$0.603191\pi$
$618$	−1.55032e7	−1.63286
$619$	4.84414e6	0.508148	0.254074	−	0.967185i	$-0.418229\pi$
$619$	4.84414e6	0.508148	0.254074	+	0.967185i	$0.418229\pi$
$620$	−5.68406e6	−0.593854
$621$	1.93869e6	0.201734
$622$	−2.51352e6	−0.260499
$623$	−6.22541e6	−0.642611
$624$	−999307.	−0.102740
$625$	390625.	0.0400000
$626$	−1.02370e7	−1.04408
$627$	−5.89950e6	−0.599303
$628$	1.79004e7	1.81119
$629$	1.50268e7	1.51440
$630$	579495.	0.0581699
$631$	−1.16421e7	−1.16401	−0.582007	−	0.813184i	$-0.697732\pi$
$631$	−1.16421e7	−1.16401	−0.582007	+	0.813184i	$0.697732\pi$
$632$	3.10120e6	0.308843
$633$	−552035.	−0.0547592
$634$	−2.51560e7	−2.48553
$635$	−5.58857e6	−0.550005
$636$	1.47683e7	1.44773
$637$	613809.	0.0599356
$638$	5.10594e6	0.496620
$639$	2.20449e6	0.213578
$640$	6.26785e6	0.604879
$641$	1.63116e7	1.56802	0.784008	−	0.620750i	$-0.213172\pi$
$641$	1.63116e7	1.56802	0.784008	+	0.620750i	$0.213172\pi$
$642$	−2.39521e7	−2.29354
$643$	6.53140e6	0.622987	0.311493	−	0.950248i	$-0.399171\pi$
$643$	6.53140e6	0.622987	0.311493	+	0.950248i	$0.399171\pi$
$644$	−1.10744e6	−0.105222
$645$	−8.25222e6	−0.781037
$646$	−2.24508e7	−2.11665
$647$	−1.13473e7	−1.06570	−0.532848	−	0.846211i	$-0.678878\pi$
$647$	−1.13473e7	−1.06570	−0.532848	+	0.846211i	$0.678878\pi$
$648$	−6.01884e6	−0.563087
$649$	−2.63380e6	−0.245455
$650$	1.42523e6	0.132312
$651$	3.22820e6	0.298543
$652$	−2.87670e7	−2.65018
$653$	1.15947e7	1.06408	0.532041	−	0.846718i	$-0.321425\pi$
$653$	1.15947e7	1.06408	0.532041	+	0.846718i	$0.321425\pi$
$654$	2.62402e7	2.39896
$655$	5.65892e6	0.515383
$656$	−3.56419e6	−0.323371
$657$	−154969.	−0.0140065
$658$	9.14649e6	0.823549
$659$	1.10765e7	0.993548	0.496774	−	0.867880i	$-0.334518\pi$
$659$	1.10765e7	0.993548	0.496774	+	0.867880i	$0.334518\pi$
$660$	3.07864e6	0.275105
$661$	1.98578e7	1.76778	0.883888	−	0.467699i	$-0.154917\pi$
$661$	1.98578e7	1.76778	0.883888	+	0.467699i	$0.154917\pi$
$662$	5.38454e6	0.477534
$663$	−3.89187e6	−0.343854
$664$	5.91952e6	0.521034
$665$	−2.79142e6	−0.244778
$666$	6.43579e6	0.562233
$667$	1.44796e6	0.126020
$668$	−3.14832e6	−0.272985
$669$	−5.34777e6	−0.461963
$670$	7.44861e6	0.641044
$671$	678348.	0.0581630
$672$	−4.70916e6	−0.402272
$673$	9.87863e6	0.840735	0.420368	−	0.907354i	$-0.361901\pi$
$673$	9.87863e6	0.840735	0.420368	+	0.907354i	$0.361901\pi$
$674$	9.77602e6	0.828919
$675$	−2.55011e6	−0.215427
$676$	−1.45521e7	−1.22478
$677$	3.21637e6	0.269708	0.134854	−	0.990865i	$-0.456943\pi$
$677$	3.21637e6	0.269708	0.134854	+	0.990865i	$0.456943\pi$
$678$	1.88865e7	1.57789
$679$	650619.	0.0541567
$680$	3.83398e6	0.317963
$681$	1.03252e7	0.853158
$682$	−8.00894e6	−0.659347
$683$	−1.96620e7	−1.61278	−0.806390	−	0.591384i	$-0.798582\pi$
$683$	−1.96620e7	−1.61278	−0.806390	+	0.591384i	$0.798582\pi$
$684$	−5.74822e6	−0.469779
$685$	1.46091e6	0.118959
$686$	1.04942e6	0.0851414
$687$	1.85602e7	1.50035
$688$	−6.79222e6	−0.547067
$689$	5.75889e6	0.462158
$690$	1.46040e6	0.116775
$691$	−2.34799e7	−1.87068	−0.935342	−	0.353743i	$-0.884909\pi$
$691$	−2.34799e7	−1.87068	−0.935342	+	0.353743i	$0.884909\pi$
$692$	1.27346e7	1.01092
$693$	488128.	0.0386100
$694$	−2.26224e7	−1.78295
$695$	8.17241e6	0.641783
$696$	−5.83170e6	−0.456322
$697$	−1.38810e7	−1.08228
$698$	−1.17706e7	−0.914452
$699$	−3.96173e6	−0.306685
$700$	1.45670e6	0.112363
$701$	1.97577e7	1.51859	0.759297	−	0.650744i	$-0.225543\pi$
$701$	1.97577e7	1.51859	0.759297	+	0.650744i	$0.225543\pi$
$702$	−9.30429e6	−0.712591
$703$	−3.10012e7	−2.36586
$704$	9.97837e6	0.758801
$705$	−7.21064e6	−0.546388
$706$	1.50189e7	1.13403
$707$	−6.59346e6	−0.496095
$708$	9.19238e6	0.689199
$709$	−9.90890e6	−0.740304	−0.370152	−	0.928971i	$-0.620694\pi$
$709$	−9.90890e6	−0.740304	−0.370152	+	0.928971i	$0.620694\pi$
$710$	9.26958e6	0.690104
$711$	−1.18454e6	−0.0878772
$712$	−1.76402e7	−1.30408
$713$	−2.27120e6	−0.167314
$714$	−6.65390e6	−0.488462
$715$	1.20052e6	0.0878219
$716$	−2.02574e7	−1.47673
$717$	1.21944e7	0.885854
$718$	−1.48528e7	−1.07522
$719$	2.70713e6	0.195293	0.0976465	−	0.995221i	$-0.468869\pi$
$719$	2.70713e6	0.195293	0.0976465	+	0.995221i	$0.468869\pi$
$720$	−376019.	−0.0270320
$721$	−6.17897e6	−0.442668
$722$	2.42305e7	1.72989
$723$	3.12067e6	0.222025
$724$	−6.80503e6	−0.482485
$725$	−1.90461e6	−0.134574
$726$	−1.54621e7	−1.08875
$727$	−4.71655e6	−0.330970	−0.165485	−	0.986212i	$-0.552919\pi$
$727$	−4.71655e6	−0.330970	−0.165485	+	0.986212i	$0.552919\pi$
$728$	1.73927e6	0.121630
$729$	1.59644e7	1.11259
$730$	−651624.	−0.0452574
$731$	−2.64528e7	−1.83096
$732$	−2.36754e6	−0.163313
$733$	−5.40920e6	−0.371855	−0.185927	−	0.982563i	$-0.559529\pi$
$733$	−5.40920e6	−0.371855	−0.185927	+	0.982563i	$0.559529\pi$
$734$	−1.09227e7	−0.748321
$735$	−827315.	−0.0564875
$736$	3.31313e6	0.225447
$737$	6.27421e6	0.425491
$738$	−5.94503e6	−0.401803
$739$	−2.17165e6	−0.146278	−0.0731390	−	0.997322i	$-0.523302\pi$
$739$	−2.17165e6	−0.146278	−0.0731390	+	0.997322i	$0.523302\pi$
$740$	1.61779e7	1.08603
$741$	8.02914e6	0.537185
$742$	9.84592e6	0.656518
$743$	−1.51671e7	−1.00793	−0.503966	−	0.863723i	$-0.668126\pi$
$743$	−1.51671e7	−1.00793	−0.503966	+	0.863723i	$0.668126\pi$
$744$	9.14733e6	0.605846
$745$	1.04332e6	0.0688692
$746$	2.80660e7	1.84644
$747$	−2.26103e6	−0.148253
$748$	9.86869e6	0.644919
$749$	−9.54636e6	−0.621775
$750$	−1.92097e6	−0.124701
$751$	−1.02102e7	−0.660595	−0.330298	−	0.943877i	$-0.607149\pi$
$751$	−1.02102e7	−0.660595	−0.330298	+	0.943877i	$0.607149\pi$
$752$	−5.93492e6	−0.382710
$753$	2.11353e6	0.135838
$754$	−6.94912e6	−0.445145
$755$	−5.94870e6	−0.379800
$756$	−9.50975e6	−0.605152
$757$	2.62320e7	1.66376	0.831881	−	0.554953i	$-0.187264\pi$
$757$	2.62320e7	1.66376	0.831881	+	0.554953i	$0.187264\pi$
$758$	2.90598e7	1.83705
$759$	1.23014e6	0.0775087
$760$	−7.90970e6	−0.496737
$761$	−1.38917e7	−0.869548	−0.434774	−	0.900540i	$-0.643172\pi$
$761$	−1.38917e7	−0.869548	−0.434774	+	0.900540i	$0.643172\pi$
$762$	2.74829e7	1.71465
$763$	1.04583e7	0.650355
$764$	−2.14728e7	−1.33093
$765$	−1.46443e6	−0.0904723
$766$	4.13213e7	2.54449
$767$	3.58457e6	0.220013
$768$	−7.39395e6	−0.452349
$769$	−2.21046e7	−1.34793	−0.673963	−	0.738765i	$-0.735409\pi$
$769$	−2.21046e7	−1.34793	−0.673963	+	0.738765i	$0.735409\pi$
$770$	2.05251e6	0.124755
$771$	−1.35019e7	−0.818010
$772$	3.72741e7	2.25094
$773$	−1.31186e7	−0.789658	−0.394829	−	0.918755i	$-0.629196\pi$
$773$	−1.31186e7	−0.789658	−0.394829	+	0.918755i	$0.629196\pi$
$774$	−1.13294e7	−0.679756
$775$	2.98748e6	0.178670
$776$	1.84358e6	0.109902
$777$	−9.18804e6	−0.545972
$778$	1.72368e7	1.02096
$779$	2.86372e7	1.69078
$780$	−4.18999e6	−0.246591
$781$	7.80808e6	0.458054
$782$	4.68135e6	0.273750
$783$	1.24338e7	0.724771
$784$	−680945.	−0.0395660
$785$	−9.40827e6	−0.544924
$786$	−2.78288e7	−1.60671
$787$	1.18124e7	0.679830	0.339915	−	0.940456i	$-0.389602\pi$
$787$	1.18124e7	0.679830	0.339915	+	0.940456i	$0.389602\pi$
$788$	3.33584e7	1.91377
$789$	−1.09821e7	−0.628050
$790$	−4.98084e6	−0.283945
$791$	7.52742e6	0.427765
$792$	1.38315e6	0.0783529
$793$	−923223.	−0.0521343
$794$	2.31601e7	1.30373
$795$	−7.76204e6	−0.435570
$796$	2.23401e7	1.24969
$797$	1.90871e7	1.06437	0.532187	−	0.846627i	$-0.321370\pi$
$797$	1.90871e7	1.06437	0.532187	+	0.846627i	$0.321370\pi$
$798$	1.37274e7	0.763097
$799$	−2.31139e7	−1.28088
$800$	−4.35801e6	−0.240749
$801$	6.73787e6	0.371057
$802$	−6.27624e6	−0.344559
$803$	−548884.	−0.0300395
$804$	−2.18980e7	−1.19471
$805$	582057.	0.0316575
$806$	1.09001e7	0.591005
$807$	−67274.3	−0.00363635
$808$	−1.86830e7	−1.00674
$809$	−1.98887e7	−1.06840	−0.534201	−	0.845357i	$-0.679388\pi$
$809$	−1.98887e7	−1.06840	−0.534201	+	0.845357i	$0.679388\pi$
$810$	9.66685e6	0.517693
$811$	2.03939e7	1.08880	0.544400	−	0.838826i	$-0.316757\pi$
$811$	2.03939e7	1.08880	0.544400	+	0.838826i	$0.316757\pi$
$812$	−7.10257e6	−0.378029
$813$	2.42726e7	1.28792
$814$	2.27949e7	1.20581
$815$	1.51196e7	0.797345
$816$	4.31755e6	0.226992
$817$	5.45735e7	2.86040
$818$	−5.49796e7	−2.87288
$819$	−664335.	−0.0346081
$820$	−1.49443e7	−0.776140
$821$	6.33190e6	0.327851	0.163925	−	0.986473i	$-0.447584\pi$
$821$	6.33190e6	0.327851	0.163925	+	0.986473i	$0.447584\pi$
$822$	−7.18428e6	−0.370855
$823$	−1.12411e6	−0.0578510	−0.0289255	−	0.999582i	$-0.509209\pi$
$823$	−1.12411e6	−0.0578510	−0.0289255	+	0.999582i	$0.509209\pi$
$824$	−1.75086e7	−0.898323
$825$	−1.61810e6	−0.0827695
$826$	6.12851e6	0.312539
$827$	−1.80423e7	−0.917334	−0.458667	−	0.888608i	$-0.651673\pi$
$827$	−1.80423e7	−0.917334	−0.458667	+	0.888608i	$0.651673\pi$
$828$	1.19860e6	0.0607572
$829$	9.66779e6	0.488586	0.244293	−	0.969701i	$-0.421444\pi$
$829$	9.66779e6	0.488586	0.244293	+	0.969701i	$0.421444\pi$
$830$	−9.50733e6	−0.479031
$831$	899312.	0.0451760
$832$	−1.35804e7	−0.680151
$833$	−2.65198e6	−0.132421
$834$	−4.01894e7	−2.00077
$835$	1.65472e6	0.0821315
$836$	−2.03596e7	−1.00752
$837$	−1.95031e7	−0.962257
$838$	3.24017e7	1.59389
$839$	1.65708e7	0.812713	0.406357	−	0.913715i	$-0.366799\pi$
$839$	1.65708e7	0.812713	0.406357	+	0.913715i	$0.366799\pi$
$840$	−2.34426e6	−0.114632
$841$	−1.12247e7	−0.547247
$842$	−5.02280e7	−2.44155
$843$	−1.78102e7	−0.863177
$844$	−1.90512e6	−0.0920588
$845$	7.64844e6	0.368494
$846$	−9.89939e6	−0.475535
$847$	−6.16260e6	−0.295159
$848$	−6.38877e6	−0.305090
$849$	−9.40980e6	−0.448034
$850$	−6.15774e6	−0.292331
$851$	6.46425e6	0.305981
$852$	−2.72514e7	−1.28615
$853$	706241.	0.0332338	0.0166169	−	0.999862i	$-0.494710\pi$
$853$	706241.	0.0332338	0.0166169	+	0.999862i	$0.494710\pi$
$854$	−1.57843e6	−0.0740594
$855$	3.02120e6	0.141340
$856$	−2.70503e7	−1.26179
$857$	−3.65006e7	−1.69765	−0.848824	−	0.528675i	$-0.822689\pi$
$857$	−3.65006e7	−1.69765	−0.848824	+	0.528675i	$0.822689\pi$
$858$	−5.90377e6	−0.273786
$859$	1.47414e6	0.0681640	0.0340820	−	0.999419i	$-0.489149\pi$
$859$	1.47414e6	0.0681640	0.0340820	+	0.999419i	$0.489149\pi$
$860$	−2.84791e7	−1.31305
$861$	8.48742e6	0.390182
$862$	−1.09047e7	−0.499859
$863$	−106412.	−0.00486365	−0.00243182	−	0.999997i	$-0.500774\pi$
$863$	−106412.	−0.00486365	−0.00243182	+	0.999997i	$0.500774\pi$
$864$	2.84504e7	1.29659
$865$	−6.69315e6	−0.304152
$866$	5.25447e7	2.38086
$867$	−2.75468e6	−0.124458
$868$	1.11408e7	0.501898
$869$	−4.19553e6	−0.188468
$870$	9.36628e6	0.419536
$871$	−8.53912e6	−0.381389
$872$	2.96344e7	1.31979
$873$	−704176.	−0.0312713
$874$	−9.65789e6	−0.427665
$875$	−765625.	−0.0338062
$876$	1.91569e6	0.0843463
$877$	−3.02178e7	−1.32667	−0.663336	−	0.748322i	$-0.730860\pi$
$877$	−3.02178e7	−1.32667	−0.663336	+	0.748322i	$0.730860\pi$
$878$	227.838	9.97449e−6 0
$879$	1.65089e7	0.720688
$880$	−1.33182e6	−0.0579749
$881$	−3.40925e7	−1.47985	−0.739927	−	0.672687i	$-0.765140\pi$
$881$	−3.40925e7	−1.47985	−0.739927	+	0.672687i	$0.765140\pi$
$882$	−1.13581e6	−0.0491625
$883$	−5.70380e6	−0.246186	−0.123093	−	0.992395i	$-0.539281\pi$
$883$	−5.70380e6	−0.246186	−0.123093	+	0.992395i	$0.539281\pi$
$884$	−1.34312e7	−0.578073
$885$	−4.83142e6	−0.207356
$886$	4.02674e7	1.72333
$887$	1.48033e7	0.631755	0.315877	−	0.948800i	$-0.397701\pi$
$887$	1.48033e7	0.631755	0.315877	+	0.948800i	$0.397701\pi$
$888$	−2.60350e7	−1.10796
$889$	1.09536e7	0.464839
$890$	2.83318e7	1.19895
$891$	8.14271e6	0.343617
$892$	−1.84556e7	−0.776633
$893$	4.76853e7	2.00104
$894$	−5.13071e6	−0.214701
$895$	1.06471e7	0.444296
$896$	−1.22850e7	−0.511216
$897$	−1.67421e6	−0.0694749
$898$	2.79313e7	1.15585
$899$	−1.45664e7	−0.601107
$900$	−1.57661e6	−0.0648810
$901$	−2.48815e7	−1.02109
$902$	−2.10567e7	−0.861736
$903$	1.61744e7	0.660097
$904$	2.13295e7	0.868080
$905$	3.57665e6	0.145163
$906$	2.92539e7	1.18403
$907$	−9.02396e6	−0.364233	−0.182116	−	0.983277i	$-0.558295\pi$
$907$	−9.02396e6	−0.364233	−0.182116	+	0.983277i	$0.558295\pi$
$908$	3.56330e7	1.43429
$909$	7.13621e6	0.286456
$910$	−2.79344e6	−0.111824
$911$	−2.63736e7	−1.05287	−0.526433	−	0.850217i	$-0.676471\pi$
$911$	−2.63736e7	−1.05287	−0.526433	+	0.850217i	$0.676471\pi$
$912$	−8.90733e6	−0.354618
$913$	−8.00834e6	−0.317955
$914$	8.26124e6	0.327100
$915$	1.24436e6	0.0491351
$916$	6.40528e7	2.52232
$917$	−1.10915e7	−0.435578
$918$	4.01995e7	1.57440
$919$	1.48682e7	0.580723	0.290362	−	0.956917i	$-0.406224\pi$
$919$	1.48682e7	0.580723	0.290362	+	0.956917i	$0.406224\pi$
$920$	1.64930e6	0.0642437
$921$	2.41107e7	0.936614
$922$	1.59377e7	0.617444
$923$	−1.06267e7	−0.410576
$924$	−6.03414e6	−0.232507
$925$	−8.50293e6	−0.326749
$926$	−3.86580e7	−1.48153
$927$	6.68760e6	0.255606
$928$	2.12488e7	0.809962
$929$	−7.00674e6	−0.266365	−0.133182	−	0.991092i	$-0.542520\pi$
$929$	−7.00674e6	−0.266365	−0.133182	+	0.991092i	$0.542520\pi$
$930$	−1.46915e7	−0.557005
$931$	5.47119e6	0.206875
$932$	−1.36722e7	−0.515585
$933$	−3.88381e6	−0.146068
$934$	7.17356e7	2.69071
$935$	−5.18687e6	−0.194033
$936$	−1.88244e6	−0.0702316
$937$	3.25355e7	1.21062	0.605311	−	0.795989i	$-0.293049\pi$
$937$	3.25355e7	1.21062	0.605311	+	0.795989i	$0.293049\pi$
$938$	−1.45993e7	−0.541781
$939$	−1.58178e7	−0.585440
$940$	−2.48845e7	−0.918564
$941$	−3.72310e7	−1.37066	−0.685332	−	0.728231i	$-0.740343\pi$
$941$	−3.72310e7	−1.37066	−0.685332	+	0.728231i	$0.740343\pi$
$942$	4.62670e7	1.69881
$943$	−5.97132e6	−0.218671
$944$	−3.97663e6	−0.145240
$945$	4.99822e6	0.182069
$946$	−4.01275e7	−1.45785
$947$	1.34378e7	0.486913	0.243457	−	0.969912i	$-0.421719\pi$
$947$	1.34378e7	0.486913	0.243457	+	0.969912i	$0.421719\pi$
$948$	1.46431e7	0.529189
$949$	747025.	0.0269258
$950$	1.27038e7	0.456692
$951$	−3.88703e7	−1.39369
$952$	−7.51459e6	−0.268728
$953$	4.30996e7	1.53724	0.768618	−	0.639708i	$-0.220945\pi$
$953$	4.30996e7	1.53724	0.768618	+	0.639708i	$0.220945\pi$
$954$	−1.06564e7	−0.379088
$955$	1.12859e7	0.400431
$956$	4.20838e7	1.48926
$957$	7.88953e6	0.278465
$958$	−5.13188e7	−1.80660
$959$	−2.86337e6	−0.100538
$960$	1.83042e7	0.641022
$961$	−5.78103e6	−0.201928
$962$	−3.10236e7	−1.08082
$963$	1.03322e7	0.359027
$964$	1.07697e7	0.373259
$965$	−1.95909e7	−0.677228
$966$	−2.86238e6	−0.0986925
$967$	−1.12466e7	−0.386772	−0.193386	−	0.981123i	$-0.561947\pi$
$967$	−1.12466e7	−0.386772	−0.193386	+	0.981123i	$0.561947\pi$
$968$	−1.74622e7	−0.598977
$969$	−3.46902e7	−1.18685
$970$	−2.96097e6	−0.101043
$971$	−4.43035e7	−1.50796	−0.753981	−	0.656897i	$-0.771869\pi$
$971$	−4.43035e7	−1.50796	−0.753981	+	0.656897i	$0.771869\pi$
$972$	1.87412e7	0.636257
$973$	−1.60179e7	−0.542405
$974$	−9.45084e6	−0.319207
$975$	2.20221e6	0.0741904
$976$	1.02420e6	0.0344160
$977$	−2.11370e7	−0.708446	−0.354223	−	0.935161i	$-0.615255\pi$
$977$	−2.11370e7	−0.708446	−0.354223	+	0.935161i	$0.615255\pi$
$978$	−7.43536e7	−2.48573
$979$	2.38649e7	0.795797
$980$	−2.85513e6	−0.0949643
$981$	−1.13192e7	−0.375529
$982$	2.33122e7	0.771446
$983$	4.40635e7	1.45444	0.727218	−	0.686406i	$-0.240813\pi$
$983$	4.40635e7	1.45444	0.727218	+	0.686406i	$0.240813\pi$
$984$	2.40497e7	0.791812
$985$	−1.75328e7	−0.575786
$986$	3.00239e7	0.983502
$987$	1.41329e7	0.461782
$988$	2.77092e7	0.903092
$989$	−1.13795e7	−0.369940
$990$	−2.22147e6	−0.0720364
$991$	−3.09729e7	−1.00184	−0.500920	−	0.865494i	$-0.667005\pi$
$991$	−3.09729e7	−1.00184	−0.500920	+	0.865494i	$0.667005\pi$
$992$	−3.33299e7	−1.07536
$993$	8.32002e6	0.267764
$994$	−1.81684e7	−0.583244
$995$	−1.17417e7	−0.375987
$996$	2.79504e7	0.892770
$997$	5.65992e7	1.80332	0.901659	−	0.432448i	$-0.142350\pi$
$997$	5.65992e7	1.80332	0.901659	+	0.432448i	$0.142350\pi$
$998$	−7.10678e7	−2.25864
$999$	5.55096e7	1.75976

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.6.a.c.1.3	✓	3
3.2	odd	2		315.6.a.i.1.1		3
4.3	odd	2		560.6.a.q.1.2		3
5.2	odd	4		175.6.b.e.99.5		6
5.3	odd	4		175.6.b.e.99.2		6
5.4	even	2		175.6.a.e.1.1		3
7.6	odd	2		245.6.a.d.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.6.a.c.1.3	✓	3	1.1	even	1	trivial
175.6.a.e.1.1		3	5.4	even	2
175.6.b.e.99.2		6	5.3	odd	4
175.6.b.e.99.5		6	5.2	odd	4
245.6.a.d.1.3		3	7.6	odd	2
315.6.a.i.1.1		3	3.2	odd	2
560.6.a.q.1.2		3	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	35.a (trivial)

\(f(q)\)	\(=\)	\(q+8.91996 q^{2} +13.7828 q^{3} +47.5657 q^{4} -25.0000 q^{5} +122.942 q^{6} +49.0000 q^{7} +138.845 q^{8} -53.0335 q^{9} -222.999 q^{10} -187.840 q^{11} +655.590 q^{12} +255.647 q^{13} +437.078 q^{14} -344.571 q^{15} -283.609 q^{16} -1104.53 q^{17} -473.057 q^{18} +2278.71 q^{19} -1189.14 q^{20} +675.359 q^{21} -1675.52 q^{22} -475.149 q^{23} +1913.68 q^{24} +625.000 q^{25} +2280.36 q^{26} -4080.18 q^{27} +2330.72 q^{28} -3047.37 q^{29} -3073.56 q^{30} +4779.97 q^{31} -6972.82 q^{32} -2588.96 q^{33} -9852.39 q^{34} -1225.00 q^{35} -2522.57 q^{36} -13604.7 q^{37} +20326.0 q^{38} +3523.54 q^{39} -3471.13 q^{40} +12567.3 q^{41} +6024.17 q^{42} +23949.3 q^{43} -8934.71 q^{44} +1325.84 q^{45} -4238.31 q^{46} +20926.4 q^{47} -3908.93 q^{48} +2401.00 q^{49} +5574.97 q^{50} -15223.6 q^{51} +12160.0 q^{52} +22526.7 q^{53} -36395.0 q^{54} +4695.99 q^{55} +6803.41 q^{56} +31407.1 q^{57} -27182.5 q^{58} +14021.5 q^{59} -16389.7 q^{60} -3611.32 q^{61} +42637.1 q^{62} -2598.64 q^{63} -53121.8 q^{64} -6391.18 q^{65} -23093.4 q^{66} -33402.0 q^{67} -52537.9 q^{68} -6548.90 q^{69} -10926.9 q^{70} -41567.8 q^{71} -7363.44 q^{72} +2922.09 q^{73} -121353. q^{74} +8614.27 q^{75} +108388. q^{76} -9204.14 q^{77} +31429.8 q^{78} +22335.7 q^{79} +7090.22 q^{80} -43349.3 q^{81} +112100. q^{82} +42634.0 q^{83} +32123.9 q^{84} +27613.3 q^{85} +213627. q^{86} -42001.4 q^{87} -26080.6 q^{88} -127049. q^{89} +11826.4 q^{90} +12526.7 q^{91} -22600.8 q^{92} +65881.5 q^{93} +186663. q^{94} -56967.8 q^{95} -96105.2 q^{96} +13277.9 q^{97} +21416.8 q^{98} +9961.79 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{2} + 26 q^{3} + 112 q^{4} - 75 q^{5} - 96 q^{6} + 147 q^{7} - 120 q^{8} + 489 q^{9} + 150 q^{10} - 194 q^{11} + 2956 q^{12} + 1892 q^{13} - 294 q^{14} - 650 q^{15} + 1496 q^{16} - 184 q^{17}+ \cdots - 60752 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 + 26 * q^3 + 112 * q^4 - 75 * q^5 - 96 * q^6 + 147 * q^7 - 120 * q^8 + 489 * q^9 + 150 * q^10 - 194 * q^11 + 2956 * q^12 + 1892 * q^13 - 294 * q^14 - 650 * q^15 + 1496 * q^16 - 184 * q^17 - 6078 * q^18 + 1212 * q^19 - 2800 * q^20 + 1274 * q^21 - 872 * q^22 + 3188 * q^23 - 13920 * q^24 + 1875 * q^25 - 9836 * q^26 + 7910 * q^27 + 5488 * q^28 - 11332 * q^29 + 2400 * q^30 + 9200 * q^31 - 20256 * q^32 - 8278 * q^33 - 18492 * q^34 - 3675 * q^35 + 38236 * q^36 + 6042 * q^37 + 25520 * q^38 + 12842 * q^39 + 3000 * q^40 + 10442 * q^41 - 4704 * q^42 + 28112 * q^43 - 20436 * q^44 - 12225 * q^45 - 41856 * q^46 + 2330 * q^47 + 68808 * q^48 + 7203 * q^49 - 3750 * q^50 + 3622 * q^51 + 63524 * q^52 + 7190 * q^53 - 138960 * q^54 + 4850 * q^55 - 5880 * q^56 + 45508 * q^57 + 37260 * q^58 + 23760 * q^59 - 73900 * q^60 + 8722 * q^61 + 24848 * q^62 + 23961 * q^63 + 4976 * q^64 - 47300 * q^65 + 24368 * q^66 - 97572 * q^67 + 3564 * q^68 + 92596 * q^69 + 7350 * q^70 - 52816 * q^71 - 251640 * q^72 + 34870 * q^73 - 241892 * q^74 + 16250 * q^75 + 115256 * q^76 - 9506 * q^77 - 142096 * q^78 - 71546 * q^79 - 37400 * q^80 - 3957 * q^81 + 241908 * q^82 - 20920 * q^83 + 144844 * q^84 + 4600 * q^85 + 266024 * q^86 - 112298 * q^87 + 59200 * q^88 - 192622 * q^89 + 151950 * q^90 + 92708 * q^91 + 248952 * q^92 - 20392 * q^93 + 360128 * q^94 - 30300 * q^95 - 296256 * q^96 + 116320 * q^97 - 14406 * q^98 - 60752 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more